چکیده انگلیسی

An important economic insight is that observed equity prices must equal the present value of the cash flows associated with the equity claim. An implication of this insight is that present values of cash flows must also quantitatively justify the observed volatility and cross-correlations of asset returns. In this paper, we show that parametric economic models for present values can indeed account for the observed high ex post return volatility and cross-correlation observed across five major equity markets—the U.S., the U.K., France, Germany, and Japan. We present evidence that cash flow growth rates contain a small predictable long-run component; this feature, in conjunction with time-varying systematic risk, can justify key empirical characteristics of observed equity prices. Our model also has direct implications for the level of equity prices and specific versions of the model can, in many cases, capture observed price levels. Our evidence suggests that the ex ante risk premium on the global market portfolio has dropped considerably—we show that this fall in the risk premium is related to a decline in the conditional variance of global real cash flow growth rates.

مقدمه انگلیسی

An important economic insight is that observed equity prices should equal the present value of the cash flows associated with the ownership of the equity claim. The work of Shiller (1981), LeRoy and Porter (1981), West (1988), and Campbell and Shiller 1987, Campbell and Shiller 1988a and Campbell and Shiller 1988b, however, poses a challenge to this insight. These authors document the “volatility puzzle”—quantitatively, equity prices are far too volatile to be justified as present values of fundamental cash flows. This result underscores the key feature of the data that cash flow volatility is quite small relative to equity price volatility. In addition to implications for volatility, present values also restrict cross-correlations of asset returns. In the data, the average cross-correlation in ex post returns is about six times larger than that for the cash flow growth rates. This feature poses an additional quantitative challenge to present values, and is labeled the “correlation puzzle”. Present values of the cash flows are determined by the time-series dynamics of the expected cash flow growth rates and the cost of capital (i.e., ex ante rate of return). In this paper, we show that a parsimonious time-series model for cash flow growth rates and the cost of capital goes a long way in explaining the observed equity market volatility and return cross-correlations.
The main insights that this paper provides can best be understood by first considering the role of the cash flow dynamics, followed by that of fluctuations in the cost of capital. In the data, real growth rates have near zero autocorrelation, hence, it is common to assume that cash flow growth rates are i.i.d. In addition to this assumption, if cost of capital is constant, then news regarding cash flow growth rates is entirely transitory and does not alter future expected growth rates. Consequently, dividend yields are constant and ex post continuous return volatility equals the growth rate volatility. However, as cash flow growth rate volatility is smaller than return volatility, this leads to the volatility puzzle discussed above.
In sharp contrast, Barsky and DeLong (1993), argue that cash flow growth rates can be modeled as an integrated process (more precisely, an ARIMA(0,1,1) process). It is important to note that in finite samples, the Barsky and DeLong process for growth rates cannot easily be distinguished from an i.i.d. process (see Shephard and Harvey, 1980), but the economic implications for asset prices are dramatically different. Expected growth rates in this specification contain a unit root, and consequently, news regarding growth rates have large effects on dividend yields as they permanently alter future expected growth rates. 1 Campbell et al. (1997) argue that Barsky and DeLong (1993) do not provide any direct empirical support for their growth rate dynamics—further, it is not clear if an integrated growth rate process is economically plausible. In this paper, unlike Barsky and DeLong (1993), we provide empirical evidence that growth rates are well modeled as a stationary (i.e., no unit root) ARIMA(1,0,1) process. As cash flow growth rates contain a small predictable (and persistent) component, growth rate news leads to volatile changes in dividend yields and ex post returns. This structure helps address the “volatility puzzle” and the “correlation puzzle” discussed above.
With constant cost of capital for each economy, the ex post return cross-correlations across economies will be solely determined by the cash flow growth correlations. However, this is unlikely to justify return cross-correlation, as growth rate correlations across economies are quite small. One factor that may account for high return correlation is fluctuations in global risk premia—a source of common fluctuations in asset prices. This view is also consistent with Ammer and Mei (1996), who document that much of the asset return covariation between national stock markets is related to news about future risk premia. Indeed, relying on a simple CAPM-GARCH specification, as in Bollerslev et al. (1988), we show that fluctuating global risk premia in conjunction with the assumed cash flow dynamics can reproduce the observed ex post return cross-correlations and asset return volatility. Further, we show that the persistent component in cash flows is also needed for duplicating asset return cross-correlations—in the absence of this, asset price fluctuations are dominated by common cost of capital fluctuations, and hence asset returns are, counter-factually, almost perfectly correlated.
The asset valuation model that we develop also provides insights regarding two additional issues. First, authors, such as Ammer and Mei (1996) use cross-correlations in cash flow news and expected returns to measure economic and financial integration, respectively, across markets. However, they do not provide any economic mechanism to link these two measures of integration—in this paper, we do provide such a mechanism and show that if there is little economic integration, then financial integration will be small as well. Second, Longin and Solnik (1995) show that an important feature of global equity market data is that periods of increased market uncertainty are also associated with a rise in the conditional correlation of returns—our model, which incorporates time-varying volatility, reproduces this feature of the data as well.
Relying on the assumed cash flow growth rate dynamics and the specification for fluctuating global risk premia, our valuation model can account for about 70–80% of the volatility of asset prices (change in dividend yield or returns) and cross-correlations in asset returns. The more standard vector autoregression (VAR) methods of modeling cash flow growth rates and expected rates of returns to compute present values (as in Campbell and Shiller, 1988a) lead to asset values which have very low variability (about 40% of that in the data) and very high (with many in excess of 0.9) cross-correlation in asset returns. In finite samples, this approach fails to capture the persistent component in cash flow growth rates which leads to large asset return variability, and hence also affects asset return cross-correlations. Despite the ability of the model to explain these particularly challenging features of the observed data, the level of fundamental values implied by the model in particular time periods, especially for Japan (in the mid-1980s) and for the U.S. (in 1994–1998), are far from the observed equity prices. For other countries, such as France and U.K., the model matches the observed equity prices quite well.
Partly motivated by the failure to match the observed equity prices in specific time periods for Japan and the U.S., we develop and estimate a model in which the time-varying world market volatility process is assumed to be latent (see Taylor, 1986; Hansen and Hodrick, 1983). Using the valuation restrictions, we show that this latent volatility can be recovered from the observed world equity market prices and the expected cash flow growth of this benchmark asset. We find that modeling the systematic risk in this manner provides a significant improvement over the GARCH specification. The latent volatility model matches the observed equity prices quite well, and captures an economically significant portion of the volatility (about 80%). Additionally, it justifies almost all of the observed cross-correlation, other than for Japan. In contrast to the GARCH specification, this model suggests that the aggregate risk premium in the global economy has fallen significantly in the last decade to about 2%. This difference has important effects on measured fundamental values. We also show that much of the fall in the latent systematic risk can be attributed to a fall in the conditional world market cash flow variance. In parallel and independent work, Fama and French (2000) “back out” the risk premia from the U.S. equity index values, and also argue that the market risk premium has fallen.
In independent papers, Dumas et al. (2000) and Chue (2000) focus on the cross-correlation among equity returns. However, they do not focus on the joint implications for return volatilities, cross-covariances, the cross-section of equity premia, and the level of equity prices. As they assume different cash flow dynamics, their results and conclusions differ from those in this paper (and that in Barsky and DeLong, 1993). For example, unlike the results in this paper, they can only account for a small fraction of the observed return volatility.
The paper is organized as follows. Section 2 discusses the data used in the paper. Section 3 provides the general present value relations used in the paper, discusses our cash flow model and the evidence supporting it, and lays down the specific fundamental restrictions implied by the model. Section 4 discusses the estimation methodology, and provides the empirical findings and diagnostics. Section 5 provides evidence on the valuation implications of our model, and Section 6 presents evidence on the size of the equity premium. Finally, Section 7 provides concluding comments.

نتیجه گیری انگلیسی

We explore the extent to which parametric asset pricing models and the “efficient market hypothesis” (i.e., asset prices should equal the present value of cash flows) can justify the observed asset volatility and cross-correlation across five major international markets. The idea that asset prices should equal present values of cash flows is fundamental to finance theory, and hence its quantitative implications are of considerable importance in understanding the behavior of equity prices.
The five markets used in the study are the U.S., U.K., Germany, France, and Japan. We find that tractable asset pricing models which incorporate time-varying systematic risk in conjuction with a stochastic trend decomposition for cash flows can explain much of the observed asset volatility and cross-correlation. Our empirical evidence suggests that cash flows news affects investors’ long-run growth expectations, and hence yields large effects on fundamental present values. In economic terms, this process, for which we provide empirical evidence, increases the equity price elasticity with respect to cash flows, but also magnifies the exposure to systematic risk, hence helping to justify the asset return cross-correlations as well. Our model also captures the observed feature that conditional return correlations across markets increase during periods of elevated uncertainty and economic downturns.
Our analysis also has implications for the risk premium on the world market portfolio. In particular, we show that the risk premium on the world market portfolio has fallen considerably, approaching 2% per annum in 1998. Further, we link this decline to the fall in the volatility of world real growth rates over the last 27 years. In all, considering the implications for asset volatility, cross-correlation and risk premia, our evidence suggests that the “efficient market hypothesis” captures, at least in an economic sense, many of the important aspects of observed equity prices in global capital markets.